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Virtual COMSATS Inferential Statistics Lecture-29

This lecture provides a recap of previous lectures and covers the practice problems related to nonparametric test procedures. It discusses the distinction between parametric and nonparametric test procedures, explains commonly used nonparametric tests, and demonstrates how to perform hypothesis tests using nonparametric procedures. The lecture also includes solutions to practice problems.

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Virtual COMSATS Inferential Statistics Lecture-29

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  1. Virtual COMSATSInferential StatisticsLecture-29 Ossam Chohan Assistant Professor CIIT Abbottabad

  2. Recap of previous lectures • Practice Problems .

  3. Objective of lecture-29 • Practice Problem-5 1. Distinguish Parametric & Nonparametric Test Procedures 2. Explain commonly used Nonparametric Test Procedures 3. Perform Hypothesis Tests Using Nonparametric Procedures

  4. Practice Problem-5 • In an experiment on reaction times in seconds of two individuals A and B, measured under identical conditions, the following results were obtained: • Test the hypothesis at 0.05 Level of significance that H0: δ2A=δ2B again not equal. • If H0: δ2A=δ2B is not rejected in part a, then test the hypothesis at 0.05 that H0:μA=μB against not equal.

  5. Practice Problem-5 Solution

  6. Cont…

  7. Cont…

  8. Non parametric tests

  9. Objectives of Lecture- 1. Distinguish Parametric & Nonparametric Test Procedures 2. Explain commonly used Nonparametric Test Procedures 3. Perform Hypothesis Tests Using Nonparametric Procedures

  10. Parametric vs Nonparametric Statistics • Parametric tests usually based upon certain assumptions about the population from which the samples were drawn or picked. • Very famous assumption is the normality assumption that is data being analyzed are randomly selected from a normally distributed population. • Important restriction is that parametric test usually requires quantitative measurement that yield interval or ratio level data. • Nonparametric Statistics are based on fewer assumptions about the population and the parameters. • Sometimes called “distribution-free” statistics. • A variety of nonparametric statistics are available for use with nominal or ordinal data.

  11. Hypothesis Testing Procedures Many More Tests Exist!

  12. Non-Parametric Tests? • Non-parametric approach derive its name from the fact that there is no explicit distribution phenomena like normal, binomial, exponential,…is associated with the data. • Also known as distribution free approach. • Data can be measured on any scale.

  13. Advantages of Nonparametric Tests 1. Can be use with all scales 2. No need to follow assumptions • No involvement of population parameter • No difference in results, as exact as parametric tests. 5. Not so complex as parametric test.

  14. Disadvantages of Nonparametric Tests 1. May Waste Information If have information about assumption , then better to use parametric tests. • Large scale data handling is bit difficult. • Like Z, t, or F, tables are not easily available.

  15. Some test (parametric and non parametric)

  16. Types of non-parametric Tests • Sign test for paired data and one sample sign test. • Positive or negative values are substituted for quantitative values. • Mann-Whitney U Test or a Rank Sum Test. • Where two independent samples have been drawn from the same population. • Kruskal Wallis Test. • Rank sum test which generalizes the ANOVA. • One Sample Run Test. • Determine the randomness of samples. • Rank correlation test. • Kolmogorov-Simrnov Test. • Kendal Test of Concordance. • Median Test for Two independent samples. • Wilcoxon signed rank test.

  17. Problem-1 • A stock broker is interested to know whether the daily movement of a particular share average in the stock market showed a pattern of movement or whether these movement were purely random. For 14 business days, he noted the value of this average and compared it with the value at the close of the previous day. He noted the increase as plus (+) and decrease as minus(-). The record was as follows: • +, +, -, -, +, +, +, -, +,+,-, +,-,- • Test whether the distribution of these movement is random or not at 5% level of significance.

  18. Problem-1 Solution

  19. Some critical values of run test

  20. Problem-1 Solution

  21. Problem-2 • Some items produced by a machine are defective. If the machine following some pattern where defective items are not randomly produced throughout the process the machine needs to be adjusted. A quality control engineer wants to determine whether the sequence of defective (D) versus good (G) items is random. The data are • GGGGG, DDD, GGGGGG, DDD, GGGGGGGGGG, DDDD, GGGGGGGGGGG, DDD, GGGGGGGGGGG, DDDD. • Test whether the distribution of defective and good items is random or not at 5% level of significance.

  22. Problem-2 Solution

  23. Cont…

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